STEADY NATURAL CONVECTION IN A TILTED LONG CYLINDRICAL ENVELOPE WITH LATERAL ADIABATIC SURFACE, PART 1: THEORETICAL MODELING AND NUMERICAL TREATMENTS

The steady natural-convection heat transfer in a tilted cylindrical envelope with constant but different end temperatures (300 and 80 K) is investigated numerically with the lateral surface being adiabatic. The inner diameter of the envelope is 27.8 mm and its length/diameter ratio is 9. This is supposed to be a simplified model for the pulse tube in a pulse-tube cryocooler when the pulse tube is positioned at different orientations. The problem studied is a typical nonlinear one in that the thermophysical properties of the working fluid (helium) vary significant om the hot end to the cold end. Three-dimensional steady-state governing equations are solved with fully variable thermal properties. The high nonlinearity of the problem leads to many special characters of the convergence process, and a very peculiar convergence process is found. Initial-field dependence is also revealed. After quite a few preliminary computations, a series of convergence criteria are proposed. Grid-independence examination is c...